Guram Bezhanishvili – författare

This book presents an English translation of a classic Russian text on duality theory

for Heyting algebras. Written by Georgian mathematician Leo Esakia, the text proved

popular among Russian-speaking logicians. This translation helps make the ideas

accessible to a wider audience and pays tribute to an influential mind in mathematical

logic. 

The book discusses the theory of Heyting algebras and closure algebras, as

well as the corresponding intuitionistic and modal logics. The author introduces the

key notion of a hybrid that “crossbreeds” topology (Stone spaces) and order (Kripke

frames), resulting in the structures now known as Esakia spaces. The main theorems

include a duality between the categories of closure algebras and of hybrids, and a duality

between the categories of Heyting algebras and of so-called strict hybrids.

Esakia’s book was originally published in 1985. It was the firstof a planned two-volume monograph

on Heyting algebras. But after the collapse of the Soviet Union, the publishing house

closed and the project died with it. Fortunately, this important work now lives on in

this accessible translation. The Appendix of the book discusses the planned contents

of the lost second volume.

This volume is dedicated to Leo Esakia''s contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area.

Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Gödel-Löb provability logic GL. One chapter scrutinizes Esakia’s work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues.